if earth is one astronomical unit from the sun and has a period of 1 year, approximately how far is planet X form the sun if it has a period of 26 yearS

Answer 1

Kepler's third law says that R^3/P^2 = constant.

http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

We can choose to measure P in years and the orbital radius R in a.u.

In your case, the ratio (R^3/26^2) = 1^3/1^2 = 1
R^3 = 676
R = 8.8 a.u.